Question

question 1 | 4-2/4-3 cw rate of change / slope-intercept form
find the rate of change of the function by using two points from the table.

x	y
2	11
3	7
4	3

(there are some math symbols and a text box for input, and a need help? button at the bottom)

Explanation:

Step1: Recall the rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Let's choose two points from the table, say \((1, 15)\) and \((2, 11)\). Here, \(x_1 = 1\), \(y_1 = 15\), \(x_2 = 2\), \(y_2 = 11\).

Step2: Calculate the rate of change

Substitute the values into the formula: \(m=\frac{11 - 15}{2 - 1}=\frac{-4}{1}=-4\).
We can verify with another pair of points, e.g., \((2, 11)\) and \((3, 7)\). Then \(x_1 = 2\), \(y_1 = 11\), \(x_2 = 3\), \(y_2 = 7\).
\(m=\frac{7 - 11}{3 - 2}=\frac{-4}{1}=-4\). Similarly, other pairs will also give the same rate.

Answer:

\(-4\)